Analytic semi-device-independent entanglement quantification for bipartite quantum states

We define a property called nondegeneracy for Bell inequalities, which describes the situation that in setting, if inequality and involved local measurements are fixed, any quantum state with given dimension its orthogonal cannot violate remarkably simultaneously. By choosing proper nondegenerate inequality, we prove an unknown bipartite of dimension, based on measurement statistics only, can provide analytic lower bound entanglement formation or even distillable entanglement, making whole process semi device independent. characterize mathematical structure nondegeneracy, quite lot well-known inequalities nondegenerate. demonstrate our approach by quantifying qutrit-qutrit states their violations Collins-Gisin-Linden-Masser-Popescu inequality.